Nonlinear Spectral Characterization of Discrete Data

The explicit analytical expression of the Nonlinear Fourier Transform (NFT) of a finite set of data is provided. Then a simple recursion relation for the NFT is constructed as a function of the spectral parameter. These tools provide a complete characterization of the nonlinear coherent structures (solitons, breathers, ...) present in numerical or experimental data representing the solution, at a given value of time, of a nonlinear evolution equation (e.g. of the nonlinear Schroedinger family).